login
A240295
T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or two plus the sum of the elements above it or two plus the sum of the elements diagonally to its northwest, modulo 4
11
2, 4, 2, 8, 6, 4, 16, 26, 24, 4, 32, 90, 206, 56, 8, 64, 340, 1322, 974, 230, 8, 128, 1194, 9970, 12164, 8064, 552, 16, 256, 4424, 63892, 180886, 200864, 38252, 2270, 16, 512, 15766, 459420, 2228098, 5967512, 1867678, 316962, 5456, 32, 1024, 57754, 2983714
OFFSET
1,1
COMMENTS
Table starts
..2.....4........8..........16............32.............64............128
..2.....6.......26..........90...........340...........1194...........4424
..4....24......206........1322..........9970..........63892.........459420
..4....56......974.......12164........180886........2228098.......31650312
..8...230.....8064......200864.......5967512......144185218.....4068505132
..8...552....38252.....1867678.....109846410.....5231971212...293426742772
.16..2270...316962....31042576....3655313420...346662397488.38864331960018
.16..5456..1502948...289075166...67561324734.12734002906536
.32.22416.12468758..4812019390.2255342381120
.32.53864.59122266.44835430372
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-2)
k=2: a(n) = 12*a(n-2) -24*a(n-4) +31*a(n-6) -16*a(n-8) for n>9
k=3: [order 48] for n>50
Empirical for row n:
n=1: a(n) = 2*a(n-1)
n=2: [order 12]
n=3: [order 80] for n>81
EXAMPLE
Some solutions for n=4 k=4
..3..1..1..3....3..1..1..0....3..1..1..0....1..3..3..1....1..0..0..0
..3..2..2..0....3..0..0..0....3..2..2..1....1..0..2..0....1..0..3..3
..3..2..0..0....1..0..2..0....1..0..2..2....1..2..0..1....3..0..2..0
..1..2..0..2....3..0..0..0....3..0..2..3....3..2..0..2....1..3..2..3
CROSSREFS
Column 1 is A016116(n+1)
Row 1 is A000079
Sequence in context: A278257 A278533 A204898 * A113477 A345298 A279350
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 03 2014
STATUS
approved